\beginsection 28.2

Use the {\it definition} of derivative to calculate the derivatives of the
following functions at the indicated points.

\medskip
(a) $f(x)=x^3$ at $x=2$
\medskip
$$\eqalign{
f^\prime&=\lim_{x\rightarrow2}{f(x)-f(2)\over x-2}\cr
&=\lim_{x\rightarrow2}{x^3-8\over x-2}\cr
&=\lim_{x\rightarrow2}x^2+2x+4\cr
&=12
}$$

\medskip
(b) $g(x)=x+2$ at $x=a$
\medskip
$$\eqalign{
g^\prime(a)&=\lim_{x\rightarrow a}{g(x)-g(a)\over x-a}\cr
&=\lim_{x\rightarrow a}{x+2-a-2\over x-a}\cr
&=1
}$$
